Stochastic resonance in noisy maps as dynamical threshold-crossing systems

Interplay of noise and periodic modulation of system parameters for the logistic map in the region after the first bifurcation and for the kicked spin model with Ising anisotropy and damping is considered. For both maps two distinct symmetric states are present that correspond to different phases of the period-2 orbit of the logistic map and to disjoint attractors of the spin map. The periodic force modulates the transition probabilities from any state to the opposite one symmetrically. It follows that the maps behave as threshold-crossing systems with internal dynamics, and stochastic resonance (maximum of the signal-to-noise ratio in the signal reflecting the occurrence of jumps between the symmetric states) in both models is observed. Numerical simulations agree qualitatively with analytic results based on the adiabatic theory.